0
Research Papers: Flows in Complex Systems

Flow and Mass Transfer for an Unsteady Stagnation-Point Flow Over a Moving Wall Considering Blowing Effects

[+] Author and Article Information
Tiegang Fang

Mechanical and Aerospace
Engineering Department,
North Carolina State University,
3246 Engineering Building III–
Campus Box 7910,
911 Oval Drive,
Raleigh, NC 27695
e-mail: tfang2@ncsu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 28, 2013; final manuscript received February 3, 2014; published online May 6, 2014. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 136(7), 071103 (May 06, 2014) (7 pages) Paper No: FE-13-1342; doi: 10.1115/1.4026665 History: Received May 28, 2013; Revised February 03, 2014

In this paper, the flow and mass transfer of a two-dimensional unsteady stagnation-point flow over a moving wall, considering the coupled blowing effect from mass transfer, is studied. Similarity equations are derived and solved in a closed form. The flow solution is an exact solution to the two-dimensional unsteady Navier–Stokes equations. An analytical solution of the boundary layer mass transfer equation is obtained together with the momentum solution. The examples demonstrate the significant impacts of the blowing effects on the flow and mass transfer characteristics. A higher blowing parameter results in a lower wall stress and thicker boundary layers with less mass transfer flux at the wall. The higher wall moving parameters produce higher mass transfer flux and blowing velocity. The Schmidt parameters generate a local maximum for the mass transfer flux and blowing velocity under given wall moving and blowing parameters.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Yang, K. T., 1958, “Unsteady Laminar Boundary Layers in an Incompressible Stagnation Flow,” Trans. ASME J. Appl. Mech., 25, pp. 421–427.
Williams, J. C.III, 1968, “Nonsteady Stagnation-Point Flow,” AIAA J., 6(12), pp. 2417–2419. [CrossRef]
Jankowski, D. F., and Gersting, J. M., 1970, “Unsteady Three-Dimensional Stagnation-Point Flow,” AIAA J., 8(1), pp. 187–188. [CrossRef]
Teipel, I., 1979, “Heat Transfer in Unsteady Laminar Boundary Layers at an Incompressible Three-Dimensional Stagnation Flow,” Mech. Res. Commun., 6(1), pp. 27–32.
Wang, C. Y., 1985, “The Unsteady Oblique Stagnation Point Flow,” Phys. Fluids, 28(7), pp. 2046–2049.
Rajappa, N. R., 1979, “Nonsteady Plane Stagnation Point Flow With Hard Blowing,” Z. Angew. Math. Mech., 59(9), pp. 471–473. [CrossRef]
Burde, G. I., 1995, “Nonsteady Stagnation-Point Flows Over Permeable Surfaces: Explicit Solutions of the Navier–Stokes Equations,” ASME J. Fluids Eng., 117(1), pp. 189–191. [CrossRef]
Ludlow, D. K., Clarkson, P. A., and Bassom, A. P., 2000, “New Similarity Solutions of the Unsteady Incompressible Boundary Layer Equations,” Q. J. Mech. Appl. Math., 53(2), pp. 175–206. [CrossRef]
Ma, P. H., and Hui, W. H., 1990, “Similarity Solutions of the Two Dimensional Unsteady Boundary Layer Equations,” J. Fluid Mech., 216, pp. 537–559. [CrossRef]
Takhar, H. S., Chamkha, A. J., and Nath, G., 1999, “Unsteady Axisymmetric Stagnation-Point Flow of a Viscous Fluid on a Cylinder,” Int. J. Eng. Sci., 37(15), pp. 1943–1957. [CrossRef]
Eswara, A. T., and Nath, G., 1999, “Effect of Large Injection Rates on Unsteady Mixed Convection Flow at a Three-Dimensional Stagnation Point,” Int. J. Nonlinear Mech., 34(1), pp. 85–103. [CrossRef]
Kumari, M., and Nath, G., 2002, “Unsteady Flow and Heat Transfer of a Viscous Fluid in the Stagnation Region of a Three-Dimensional Body With a Magnetic Field,” Int. J. Eng. Sci., 40(4), pp. 411–432. [CrossRef]
Seshadri, R., Sreeshylan, N., and Nath, G., 1997, “Unsteady Three-Dimensional Stagnation Point Flow of a Viscoelastic Fluid,” Int. J. Eng. Sci., 35(5), pp. 445–454. [CrossRef]
Xu, H., Liao, S. J., and Pop, I., 2006, “Series Solution of Unsteady Boundary Layer Flows of Non-Newonian Fluids Near a Forward Stagnation Point,” J. Non-Newtonian Fluid Mech., 139(1–2), pp. 31–43. [CrossRef]
Nazar, R., Amin, N., Filip, D., and Pop, I., 2004, “Unsteady Boundary Layer Flow in the Region of the Stagnation Point on a Stretching Sheet,” Int. J. Eng. Sci., 42(11–12), pp. 1241–1253. [CrossRef]
Baris, S., and Dokuz, M. S., 2006, “Three-Dimensional Stagnation-Point Flow of a Second-Grade Fluid Towards a Moving Plate,” Int. J. Eng. Sci., 44(1–2), pp. 49–58. [CrossRef]
Fang, T., Lee, C. F., and Zhang, J., 2011, “The Boundary Layers of an Unsteady Incompressible Stagnation-Point Flow With Mass Transfer,” Int. J. Nonlinear Mech., 46(7), pp. 942–948. [CrossRef]
Zhong, Y., and Fang, T., 2011, “Unsteady Stagnation-Point Flow Over a Plate Moving Along the Direction of Flow Impingement,” Int. J. Heat Mass Transfer, 54(15–16), pp. 3103–3108. [CrossRef]
Abbassi, A. S., and Rahimi, A. B., 2012, “Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate,” ASME J. Heat Transfer, 134(6), p. 064501. [CrossRef]
Magyari, E., and Weidman, P. D., 2012, “Comment on ‘Unsteady Stagnation-Point Flow Over a Plate Moving Along the Direction of Flow Impingement,’” Int. J. Heat Mass Transfer, 55(4), pp 1423–1424. [CrossRef]
Fang, T., and Zhong, Y., 2012, “Reply to ‘Comment on “Unsteady Stagnation-Point Flow Over a Plate Moving Along the Direction of Flow Impingement,’” Int. J. Heat Mass Transfer, 55(4), pp. 1425–1426. [CrossRef]
Nellis, G., and Klein, S., 2008, Heat Transfer, Cambridge University Press, Cambridge, UK, pp. E23–E25.
Lienhard, J. H.IV, and Lienhard, J. H.V, 2005, A Heat Transfer Textbook, 3rd ed., Phlogiston Press, Cambridge, MA, pp. 662–663.
Spalding, D. B., 1954, “Mass Transfer in Laminar Flow,” Proc. R. Soc. London, Ser. A, 221, pp. 78–99. [CrossRef]
Acrivos, A., 1962, “The Asymptotic Form of the Laminar Boundary-Layer Mass-Transfer Rate for Large Interfacial Velocities,” J. Fluid Mech., 12(3), pp. 337–357. [CrossRef]
Nienow, A. W., Unahabhokha, R., and Mullin, J. W., 1969, “The Mass Transfer Driving Force for High Mass Flux,” Chem. Eng. Sci., 24(11), pp. 1655–1660. [CrossRef]
Asano, K., and Fujita, S., 1971, “Mass Transfer for a Wide Range of Driving Force Evaporation of Pure Liquids,” Chem. Eng. Sci., 26(8), pp. 1187–1194. [CrossRef]
Hasan, M., and Mujumdar, A. S., 1983, “Effect of Finite Normal Interfacial Velocity on Free Convection Heat and Mass Transfer Rates From an Inclined Plate,” Int. Commun. Heat Mass Transfer, 10(6), pp. 477–490. [CrossRef]
Loughlin, K. F., Hadley-Coates, L., and Halhouli, K., 1985, “High Mass Flux Evaporation,” Chem. Eng. Sci., 40(7), pp. 1263–1272. [CrossRef]
Boukadida, N., and Nasrallah, S. B., 2001, “Mass and Heat Transfer During Water Evaporation in Laminar Flow Inside a Rectangular Channel-Validity of Heat and Mass Transfer Analogy,” Int. J. Therm. Sci., 40(1), pp. 67–81. [CrossRef]
Czaputa, K., and Brenn, G., 2012, “The Convective Drying of Liquid Films on Slender Wires,” Int. J. Heat Mass Transfer, 55(1–3), pp. 19–31. [CrossRef]
Fang, T., and Jing, W., 2014, “Flow, Heat, and Species Transfer Over a Stretching Plate Considering Coupled Stefan Blowing Effects From Species Transfer,” Communications in Nonlinear Science and Numerical Simulation, (in press).
Wolfram, S., 1993, Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, New York.

Figures

Grahic Jump Location
Fig. 1

Schematic of the flow configuration

Grahic Jump Location
Fig. 2

Solution domain for δ as a function of the blowing parameters under different Schmidt numbers for (a) λ = 4 and (b) λ = 13

Grahic Jump Location
Fig. 3

Solution domain for δ as a function of the Schmidt numbers under different blowing parameters for (a) λ = 4 and (b) λ = 13

Grahic Jump Location
Fig. 4

Solution behavior of δ for large values of the Schmidt numbers for λ = 13 and s = 10

Grahic Jump Location
Fig. 5

Velocity and concentration profiles for different blowing parameters at λ = 4 under (a) Sc = 1 and (b) Sc = 10

Grahic Jump Location
Fig. 6

Velocity and concentration profiles for different blowing parameters at λ = 13 under (a) Sc = 1 and (b) Sc = 10

Grahic Jump Location
Fig. 7

The mass transfer flux -θ'(0) as a function of the Schmidt numbers under different blowing parameters for (a) λ = 4 and (b) λ = 13

Grahic Jump Location
Fig. 8

The blowing velocity -sθ'(0) as a function of the Schmidt numbers under different blowing parameters for (a) λ=4 and (b) λ=13

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In